PDEs with Compressed Solutions

Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity) as a constraint or penalty in a variational principle. We apply this approach to partial differential equations that come from a variational quantity, either by minimization (to obtain an elliptic PDE) or by gradient flow (to obtain a parabolic PDE). Also, we show that some PDEs can be rewritten in an $L^1$ form, such as the divisible sandpile problem and signum-Gordon. Addition of an $L^1$ term in the variational principle leads to a modified PDE where a subgradient term appears. It is known that modified PDEs of this form will often have solutions with compact support, which corresponds to the discrete solution being sparse. We show that this is advantageous numerically through the use of efficient algorithms for solving $L^1$ based problems.Comment: 21 pages, 15 figure

An L1 Penalty Method for General Obstacle Problems

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an exact regularizer in the sense that for large (but finite) penalty parameter, we recover the exact solution. Our formulation is applied to classical elliptic obstacle problems as well as some related free boundary problems, for example the two-phase membrane problem and the Hele-Shaw model. One advantage of the proposed method is that the free boundary inherent in the obstacle problem arises naturally in our energy minimization without any need for problem specific or complicated discretization. In addition, our scheme also works for nonlinear variational inequalities arising from convex minimization problems.Comment: 20 pages, 18 figure

Combined Cyclosporin A and Hypothermia Treatment Inhibits Activation of BV-2 Microglia but Induces an Inflammatory Response in an Ischemia/Reperfusion Hippocampal Slice Culture Model

Introduction: Hypothermia attenuates cerebral ischemia-induced neuronal cell death associated with neuroinflammation. The calcineurin inhibitor cyclosporin A (CsA) has been shown to be neuroprotective by minimizing activation of inflammatory pathways. Therefore, we investigated whether the combination of hypothermia and treatment with CsA has neuroprotective effects in an oxygen-glucose deprivation/reperfusion (OGD/R) injury model in neuronal and BV-2 microglia monocultures, as well as in an organotypic hippocampal slice culture (OHSC). Methods: Murine primary neurons, BV-2 microglia, and OHSC were pretreated with CsA and exposed to 1 h OGD (0.2% O2) followed by reperfusion at normothermia (37°C) or hypothermia (33.5°C). Cytotoxicity was measured by lactate dehydrogenase and glutamate releases. Damage-associated molecular patterns (DAMPs) high mobility group box 1 (HMGB1), heat shock protein 70 (Hsp70), and cold-inducible RNA-binding protein (CIRBP) were detected in cultured supernatant by western blot analysis. Interleukin-6 (IL-6), Interleukin-1α and -1β (IL-1α/IL1-β), tumor necrosis factor-α (TNF-α), monocyte chemotactic protein 1 (MCP1), inducible nitric oxide synthase (iNOS), glia activation factors ionized calcium-binding adapter molecule 1 (Iba1), and transforming growth factor β1 (TGF-β1) gene expressions were analyzed by RT-qPCR. Results: Exposure to OGD plus 10 μM CsA was sufficient to induce necrotic cell death and subsequent release of DAMPs in neurons but not BV-2 microglia. Moreover, OGD/R-induced secondary injury was also observed only in the neurons, which was not attenuated by cooling and no increased toxicity by CsA was observed. BV-2 microglia were not sensitive to OGD/R-induced injury but were susceptible to CsA-induced toxicity in a dose dependent manner, which was minimized by hypothermia. CsA attenuated IL-1β and Iba1 expressions in BV-2 microglia exposed to OGD/R. Hypothermia reduced IL-1β and iNOS expressions but induced TNF-α and Iba1 expressions in the microglia. However, these observations did not translate to the ex vivo OHCS model, as general high expressions of most cytokines investigated were observed. Conclusion: Treatment with CsA has neurotoxic effects on primary neurons exposed to OGD but could inhibit BV-2 microglia activation. However, CsA and hypothermia treatment after ischemia/reperfusion injury results in cytotoxic neuroinflammation in the complex ex vivo OHSC

Quantum Gauss Jordan Elimination

In this paper we construct the Quantum Gau\ss Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order $2^{N/2}$

Post-TTM Rebound Pyrexia after Ischemia-Reperfusion Injury Results in Sterile Inflammation and Apoptosis in Cardiomyocytes

Introduction. Fever is frequently observed after acute ischemic events and is associated with poor outcome and higher mortality. Targeted temperature management (TTM) is recommended for neuroprotection in comatose cardiac arrest survivors, but pyrexia after rewarming is proven to be detrimental in clinical trials. However, the cellular mechanisms and kinetics of post- TTM rebound pyrexia remain to be elucidated. Therefore, we investigated the effects of cooling and post-TTM pyrexia on the inflammatory response and apoptosis in a cardiomyocyte ischemia-reperfusion (IR) injury model. Methods. HL-1 cardiomyocytes were divided into the following groups to investigate the effect of oxygen-glucose deprivation/reperfusion (OGD/R), hypothermia (33.5°C), and pyrexia (40°C): normoxia controls maintained at 37°C and warmed to 40°C, OGD/R groups maintained at 37°C and cooled to 33.5°C for 24 h with rewarming to 37°C, and OGD/R pyrexia groups further warmed from 37 to 40°C. Caspase-3 and RBM3 were assessed by Western blot and TNF-α, IL-6, IL-1β, SOCS3, iNOS, and RBM3 transcriptions by RT-qPCR. Results. OGD-induced oxidative stress (iNOS) in cardiomyocytes was attenuated post-TTM by cooling. Cytokine transcriptions were suppressed by OGD, while reperfusion induced significant TNF-α transcription that was exacerbated by cooling. Significant inductions of TNF-α, IL-6, IL-1β, and SOCS3 were observed in noncooled, but not in cooled and rewarmed, OGD/R-injured cardiomyocytes. Further warming to pyrexia induced a sterile inflammatory response in OGD/R-injured groups that was attenuated by previous cooling, but no inflammation was observed in pyrexic normoxia groups. Moreover, cytoprotective RBM3 expression was induced by cooling but suppressed by pyrexia, correlating with apoptotic caspase-3 activation. Conclusion. Our findings show that maintaining a period of post-TTM “therapeutic normothermia” is effective in preventing secondary apoptosis-driven myocardial cell death, thus minimizing the infarct area and further release of mediators of the innate sterile inflammatory response after acute IR injury

Superconductivity at 2.3 K in the misfit compound (PbSe)1.16(TiSe2)2

The structural misfit compound (PbSe)1.16(TiSe2)2 is reported. It is a superconductor with a Tc of 2.3 K. (PbSe)1.16(TiSe2)2 derives from a parent compound, TiSe2, which shows a charge density wave transition and no superconductivity. The crystal structure, characterized by high resolution electron microscopy and powder x-ray diffraction, consists of two layers of 1T-TiSe2 alternating with a double layer of (100) PbSe. Transport measurements suggest that the superconductivity is induced by charge transfer from the PbSe layers to the TiSe2 layers.Comment: 17 pages, 4 figures. To be published in Physical Review

A simple, high throughput method to locate single copy sequences from Bacterial Artificial Chromosome (BAC) libraries using High Resolution Melt analysis

BACKGROUND: The high-throughput anchoring of genetic markers into contigs is required for many ongoing physical mapping projects. Multidimentional BAC pooling strategies for PCR-based screening of large insert libraries is a widely used alternative to high density filter hybridisation of bacterial colonies. To date, concerns over reliability have led most if not all groups engaged in high throughput physical mapping projects to favour BAC DNA isolation prior to amplification by conventional PCR. RESULTS: Here, we report the first combined use of Multiplex Tandem PCR (MT-PCR) and High Resolution Melt (HRM) analysis on bacterial stocks of BAC library superpools as a means of rapidly anchoring markers to BAC colonies and thereby to integrate genetic and physical maps. We exemplify the approach using a BAC library of the model plant Arabidopsis thaliana. Super pools of twenty five 384-well plates and two-dimension matrix pools of the BAC library were prepared for marker screening. The entire procedure only requires around 3 h to anchor one marker. CONCLUSIONS: A pre-amplification step during MT-PCR allows high multiplexing and increases the sensitivity and reliability of subsequent HRM discrimination. This simple gel-free protocol is more reliable, faster and far less costly than conventional PCR screening. The option to screen in parallel 3 genetic markers in one MT-PCR-HRM reaction using templates from directly pooled bacterial stocks of BAC-containing bacteria further reduces time for anchoring markers in physical maps of species with large genomes

Peningkatan Aktivitas Pembelajaran dan Hasil Belajar Pendidikan Kewarganegaraan dengan Metode Diskusi Kelompok pada Siswa Kelas IV S Ekolah Dasar Negeri 03 Semayang Kabupaten Sanggau

The pourpose of the research iis to know the improving studeng activity of civics at grade IV student of SD 03 Semayang by using group discussion method. The method of this research is descriptive method using qualitative way in which the data or evidence is analyzed after collecting the data from the field. The subject of the research is 22 students of grade IV at elementary school 03 Semayang. The result of data analyzing show that after using group discussion method for 2 cycles, the student learning activity improves 19% at first cycles become 59 at second cycles. Increasing the presentage of student learning activity influences the improving students outcome in achiving KKM of Civic at school that is 60. In wich, the research shows that the student can achive KKm about 41% at first cycle increase 91% at the second cycle. So that, it can be conduded that by improving student learning activity using group discussion method can influence the improving student aoutcome at grade IV student of elementary school 03 Semayang

Complement activation in inflammatory skin diseases

The complement system is a fundamental part of the innate immune system, playing a crucial role in host defense against various pathogens, such as bacteria, viruses, and fungi. Activation of complement results in production of several molecules mediating chemotaxis, opsonization, and mast cell degranulation, which can contribute to the elimination of pathogenic organisms and inflammation. Furthermore, the complement system also has regulating properties in inflammatory and immune responses. Complement activity in diseases is rather complex and may involve both aberrant expression of complement and genetic deficiencies of complement components or regulators. The skin represents an active immune organ with complex interactions between cellular components and various mediators. Complement involvement has been associated with several skin diseases, such as psoriasis, lupus erythematosus, cutaneous vasculitis, urticaria, and bullous dermatoses. Several triggers including auto-antibodies and micro-organisms can activate complement, while on the other hand complement deficiencies can contribute to impaired immune complex clearance, leading to disease. This review provides an overview of the role of complement in inflammatory skin diseases and discusses complement factors as potential new targets for therapeutic intervention

BAC-HAPPY mapping (BAP mapping): a new and efficient protocol for physical mapping

Physical and linkage mapping underpin efforts to sequence and characterize the genomes of eukaryotic organisms by providing a skeleton framework for whole genome assembly. Hitherto, linkage and physical “contig” maps were generated independently prior to merging. Here, we develop a new and easy method, BAC HAPPY MAPPING (BAP mapping), that utilizes BAC library pools as a HAPPY mapping panel together with an Mbp-sized DNA panel to integrate the linkage and physical mapping efforts into one pipeline. Using Arabidopsis thaliana as an exemplar, a set of 40 Sequence Tagged Site (STS) markers spanning ~10% of chromosome 4 were simultaneously assembled onto a BAP map compiled using both a series of BAC pools each comprising 0.7x genome coverage and dilute (0.7x genome) samples of sheared genomic DNA. The resultant BAP map overcomes the need for polymorphic loci to separate genetic loci by recombination and allows physical mapping in segments of suppressed recombination that are difficult to analyze using traditional mapping techniques. Even virtual “BAC-HAPPY-mapping” to convert BAC landing data into BAC linkage contigs is possible.Giang T. H. Vu, Paul H. Dear, Peter D. S. Caligari and Mike J. Wilkinso